Sum-day Soon

Some people believe that January 1, 2000 is the first day of the 21st century. Other people believe that the honor belongs to January 1, 2001. But everyone should agree that January 1, 2002 is the first "sum-day" of the new century- when you write out that date in standard notation, it becomes 01/01/02, and 1+1=2. More generally, a sum-day is a date in which the day and month add up to the year. With that in mind:

A) What is the last sum-day of the 21st century?

B) How many sum-days are there in the 21st century?

Answer

A) The last sum-day of the 21st century is December 31, 2043, because 12+31=43, and both the month and day are as big as possible.

B) This one is much easier than you might think. The correct answer is 365, because every day in a standard (non-leap) year is part of a sum-day for some year. For example, November 26 is a sum-day for the year 2037, because 11+26=37. The only date for which this principle doesn't work is the leap day, February 29. That's because 2+29=31, but 2031 is not a leap year.Hide

actual answer 355. Starting in 2002 there is only one day - 1/1/02. Whatever formula used does not seem to take into account the all months do not end with the same number.

There are two in 2003.
This number increases by one each year until 2013 where there are 12 per year until 2032.

Beginning in 2033 it drops by two to 10 because February ends with 28 days.
Every two tears beginning in 2033 the total drops by 2 until 2039 where there are five days
Then it continues dropping by two until 2042 where there is one day and then the last day 12/31/43.
So the breakdown goes like this :

Too easy, once I saw the easy way to do it. I mean, it would be a pointless teaser to ask something like "add up the first 1000 primes", when there's no easy way to do that like there is the first 1000 numbers, squares, triangles, Fibanoccis, etc.

the method for part b is much easier than that way I went at it. I did more like BigTexas27, above. I think he had too many days in 2032 and 2031. Also, got a different total. I got the 365 the hard way.

HUH?!?!?... i am sure this is a good teaser, but what would make me want to sit down and figure this out???... i have been out of school for 15 years now, and what you guys are learning in school is great, dont get me wrong, but when you never learned a simple equation to figure this out, it it kinda hard to understand what you are talking about... in other words, i am completely lost

By definition, the only "variable" in figuring out a sum-day is the year. Given any month/day combination, the sum-day occurs during the year which is the sum of the given month and day. By this logic, at most there can be 365 sum-days.

To figure out how many there are, just subtract any month/day combinations that don't have a given year to make a sum-day. Since there are none, 365-0 = 365.

To be more explicit, the following is a list of all the sum-days in the 21st century (gotta love Excel!):

Fascinating teaser - I admire people who figured this one out - especially those who didn't use a calculator!
However it's not my thing and I was only half awake when I tried it.
Give me a good old word puzzle.
PS Babe, how did I beat you here today!

Not sure why we were given a calculator to figure this out. I did it using a pen and paper and had no trouble. Of course I went to school in the dark ages where until we reached the upper high school grades and more advanced maths like trig and calculus using a calculator was considered cheating and being caught with one was an auto-fail. It was a great teaser that for the people who put wanted to put in the time to figue it out, it was very doable.

Not sure why we were given a calculator to figure this out. I did it using a pen and paper and had no trouble. Of course I went to school in the dark ages where until we reached the upper high school grades and more advanced maths like trig and calculus using a calculator was considered cheating and being caught with one was an auto-fail. It was a great teaser that for the people who put wanted to put in the time to figue it out, it was very doable.

I'm with HABS on the calculator issue vis a vis school!! As for this teaser, I love math and would love to have figured this out but have a FEW other things to accomplish today! (part A of course was easy!)

I do not know where I was for this one in 2012, but glad I was missed by Gaylewolf and speaking of that person, I have not seen him or her around for a while and wonder where are you??? I did not try this one as it was way too long to sit and figure out. After I have the knowledge, what do I do with it anyway?
Glad some enjoyed it anyway.